Formula to convert binary to decimal and decimal to binary?

Answer 1

I do not know a specific formula to do it. but its very simple. really really simple

lets get a binary code = 10011101

now, we are going to convert this to decimal. You should start it from the last binary number in the given code,(right hand corner)

then multiply that number from 2 to the power of 0( 2^0)

1* (2^0) = 1* 1 = 1 --------- (A)

then we go to the next binary number. (which is 0 in this case)

now we must multiply this from 2 to the power 1. (2^1);

0 * (2^1) = 0* 2 = 0 --------(B)

do this sequentially till the first number. (multiplying from 2^2,2^3,...,2^7)

similarly you get,

1 * (2^2) = 4 ----(C)

1 * (2^3) = 8 ----(D)

1 * (2^4) = 16 ----(E)

0 * (2^5) = 0 ------(F)

0 * (2^6) = 0-----(G)

1 * (2^7) = 128----(H)

now, add the values you got in equation A,B,C,D,E,F,G,H

1+0+4+8+16+0+0+128 = 157; so this is the decimal number for the given binary code.

hope you got it!!

Answer 2

For binary to decimal, start from the right-most bit and work your way left. Each position is double the size of the position to the right of it. You can also think of each position as the exponent of a power of two:

7 6 5 4 3 2 1 0

2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0

Remember that 2^0 is 1 (as is any number raised to the zeroth power). For each 1, add the value of that position to the total; otherwise skip to the next position. For example:

0101

2^0 (1) = 1

2^1 (0) = 0

2^2 (1) = 4

2^3 (0) = 0

1+0+4+0 = 5

You can repeat this for as many bits as you need to.

For binary to decimal, you divide by two, and you place the remainder into a list. When you're done, read the remainders backwards and you have your binary number. For example:

What is 19 Decimal in Binary?

19/2 = 9 r 1

9/2 = 4 r 1

4/2 = 2 r 0

2/2 = 1 r 0

1/2 = 0 r 1

When you read this backwards, you get 10011. Typically, binary numbers will be written in multiples of 8 bits; if you need to do this, just add 0's to the left until you have 8: 00010011.